Creativity cannot be taught. It can only be encouraged and developed. As long as the teacher (or instructor) is leading, there will be no creative thought. Ask questions, listen, listen, listen, and give students time to think. Sometimes a whole class period ( an arbitrary division of time that inhibits creativity) needs to be allowed to pass before an original thought will emerge. It has been my experience that the quiet student is probably the most creative one in the room. So, ask questions...and listen to the answers.
If, as the teacher, you are uncomfortable with creativity, don't try it. Just lecture on. If you have discovered something that has brought a new thought into your head, share the trill of creativity and allow the students to "catch fire".
There are many critics, but very little critical thinking. Critical thinking results when the other person is asked why.Critical thinking is destroyed by an authoritative analysis of the answer. The critic may be right, or maybe wrong, the point is to produce an analysis that satisfies the investigator.
These two points are best served by an honest answer as to the purpose of an education. Why are we in school?
I am a fanatic of the triadic method by Sternberg where you divide your instruction into an analytical, practical, and creative dimensions to ensure understanding and the use of multiple intelligences.
Often, when I differentiate my instructional groups, I already know who is who and with whom. After I teach the lesson whole-group, I take my analytical students to perform an in-depth study of the concept online. My hands-on kids would have a project waiting where they will use the skills that are used to understand the concept.
All students are then required to use what they learned from their differentiated instruction and put it into a practical project that shows how they would implement the learned concept into their everyday lives. For instance: Division in your life. The digestive process and you. Things like that.
As long as you have a good set of rules for group conduct and clear instructions at each center you are sure to have a successful lesson.
One of the activities that I do to help students think more creatively and critically is to take a section of a famous novel or poem and to present it to the students with blanked out words. I either give them a list of suggestions (including the word the original contained) or leave them to come up with their own ideas based on the rest of the work they can see. We then talk about it in class and they have to justify the choice of word they have gone for and how it relates/impacts the overall extract.
Poetry is always a good place to start. Poetry can examine both creativity and critical thinking. For the creative side, ask students to draw (or create) an image which represents the poem. For the critical aspect of it, ask them to examine the use of figurative language, mood, symbolism, or what the poet is saying (what is the message and how well is the message stated).
I like #3's suggestion! Very good idea!
For creativity, writing! Make up stories and embellish them with detail and dialogue! Students should be able to type at an early age, since almost every part of life now involves computers, so assign them topics or even just a word or object and have them write a story about it. The more you write, the easier it is to write and think about possibilities, branches of story, of the future; you can say, "This might happen, or this, or this..." and one of them is always something that grabs your interest and you say "Ah ha! That's what I want to write about!"
Essentially, more writing = more creativity. At least, I've found that in myself.
These are abilities that are difficult and time consuming to develop in a student, but I think the best thing we can do as teachers is to create a classroom environment where creativity and critical thinking are encouraged and allowed on a daily basis. Create assignments and ask questions that provoke both critical thinking and creativity. Encourage the idea that there is not necessarily a right or wrong answer, but an merely effective and ineffective arguments. Model this when you teach, and in the questions you ask during discussion. Best of all, try to get students into smaller study groups that you can work with, where the opportunity for each student to participate and develop is greater.
I teach history to HS students as well, but I find that bringing in some examples from every day life is more helpful in getting students started on critical thinking. Later on, I move to things like primary sources. First, I'll pose scenarios like ones regarding sports. I'll bring up the example of the VB team that I coach and I'll pose an example of a problem we could be having (fictional) and ask students to critique a possible solution. Or I'll bring up the example of a student having a clash with a teacher and have us think critically about various statements about the cause of that clash. It's all about giving them situations that seem familiar and then encouraging them to think about those situations.
In the field of literature, one method that might be useful in encouraging both creative and critical thinking would be to take a famous work (preferably a short poem or very short story, or several paragraphs from a story) and ask students to substitute their own word choices for some of the choices already made by the author. Inserting their own synonyms into a work might stimulate creativity. Analyzing the different connotations of the original word and the synonym might stimulate critical thinking. To take a very trivial example: how is "It was a dark and stormy night" different in effect and in precise meaning from "The evening was black and tempestuous"?
A very common activity used to assess/enhance creative thinking is to give students, especially young students, an everyday object and to challenge them to come up with as many different uses for it as they can. Sadly, I've seen studies that show kids can come up with more uses before they enter school than after they've experienced several years of schooling. As far as critical thinking goes, it would depend on which discipline you're interested in. All academic disciplines demand critical thinking in one form or another. For my discipline, history, I'd suggest primary source analysis, particularly related to analyzing bias.
You're asking for two different types of end products, and there are lots of techniques that can be used to develop and expand either type of thought process.
I found one of the easiest exercises to develop and demonstrate creativity was to give my students a sheet filled with circles, roughly the size of a quarter - as many columns and rows as would fit on the page. The instructions were for the students to use the circles to draw as many things as they could think of. After whatever period of time I planned to give them - 15-20 minutes was usually a good length - we could stop and start analyzing.
Students could simply count how many different items they drew - that's fluency, the number of ideas created. Students could examine the different kinds of ideas they created, which is flexibility - a happy face and a sad face are still faces, as distinct from a car tire and a bicycle tire, which are tires as distinct from a planet or from a pizza. Students could look at the numbers of details added to their pictures, which is elaboration - does the pizza include different kinds of toppings, does the sad face include tears and drooping eyebrows and scraggly hair? The class as a whole could share lists of ideas so students could identify their original ideas - the creative thoughts that no one else had, such as combining two circles as wheels of a car, drawing a large circle around three of the printed circles to make eyes and a mouth of a surprised face, etc.